000			nam a22 4500
999			_c32471 _d32471
008			230831b xxu||||| |||| 00| 0 eng d
020			_a9783030509194
082			_a510 _bSMO
100			_aSmorynski, Craig
245			_aMathematical problems : an essay on their nature and importance
260			_bSpringer, _c2020 _aCham :
300			_avi, 406 p. ; _bill., _c23 cm
365			_b89.99 _cEUR _d94.90
504			_aIncludes index.
520			_aThe life and soul of any science are its problems. This is particularly true of mathematics, which, not referring to any physical reality, consists only of its problems, their solutions, and, most excitingly, the challenges they pose. Mathematical problems come in many flavours, from simple puzzles to major open problems. The problems stimulate, the stories of their successful solutions inspire, and their applications are wide. The literature abounds with books dedicated to mathematical problems — collections of problems, hints on how to solve them, and even histories of the paths to the solutions of some famous ones. The present book, aimed at the proverbial “bright high-school student”, takes a different, more philosophical approach, first dividing mathematical problems into three broad classes — puzzles, exercises, and open problems — and discussing their various roles in one’s mathematical education. Various chapters are devoted to discussing examples of each type of problem, along with their solutions and some of the developments arising from them. For the truly dedicated reader, more involved material is offered in an appendix. Mathematics does not exist in a vacuum, whence the author peppers the material with frequent extra-mathematical cultural references. The mathematics itself is elementary, for the most part pre-calculus. The few references to the calculus use the integral notation which the reader need not truly be familiar with, opting to read the integral sign as strange notation for area or as operationally defined by the appropriate buttons on his or her graphing calculator. Nothing further is required. Advance praise for Mathematical Problems "There are many books on mathematical problems, but Smoryński’s compelling book offers something unique. Firstly, it includes a fruitful classification and analysis of the nature of mathematical problems. Secondly, and perhaps most importantly, it leads the reader from clear and often amusing accounts of traditional problems to the serious mathematics that grew out of some of them." - John Baldwin, University of Illinois at Chicago "Smoryński manages to discuss the famous puzzles from the past and the new items in various modern theories with the same elegance and personality. He presents and solves puzzles and traditional topics with a laudable sense of humor. Readers of all ages and training will find the book a rich treasure chest.
650			_aBayes's theorem
650			_aBiggs Norman
650			_aCircular City Problem
650			_a Puzzles
650			_aEuler's formula
650			_aFive colour theorem
650			_aFour frogs problem
650			_aGodel's Incomplete theorem
650			_aHilber-Bernays derivability conditions
650			_a Knight's tour
650			_aLob's theorem
650			_aMonty Hall problem
650			_a Napolean's theorem
650			_aParson's puzzle
650			_aPeterburg problem
650			_aShipman's puzzle
650			_aVeritasium
942			_2ddc _cBK